Abstract

<p>Reflectances of transmissive sheets, calculated from the transmissions of one and two sheets, are compared with reflectances obtained by using the General Electric recording spectrophotometer. The expression used as a basis for calculation, <i>R</i><sub><i>a</i></sub> = (1 - <i>T</i><sub><i>a</i></sub><sup>2</sup>/T<sub>2<i>a</i></sub>)<sup>½</sup>, in which <i>R</i><sub><i>a</i></sub> is the reflectance, and <i>T</i><sub><i>a</i></sub>. and <i>T</i><sub>2<i>a</i></sub> are the transmissions of one and two sheets, respectively, of <i>a</i>, was derived by considering the infinite series of reflections undergone by light, or radiant energy in general, in passing through the two sheets. The expression was found to be valid and useful over a wide range of reflectances and wave-lengths, for materials such as paper, glass, and an organic plastic.</p><p>The method is an absolute one since it involves no reflectance standard. It involves no spherical or similar integrating device nor does it involve any reflecting surface other than that of the sample itself, as a fundamental part of the measurements. When transmission values for diffuse incidence are substituted into the expression, the reflectances thus calculated correspond to the conditions of diffuse incidence and diffuse viewing, and as such are somewhat higher than the usual directly measured reflectances for normal incidence and diffuse viewing (or diffuse incidence and normal viewing). For clear sheets, with normal incidence, specular reflectance may be calculated.</p><p>The method thus affords a means of determining, from two simple measurements, the specular-plus-diffuse reflectance of transmissive sheets for diffused light or radiant energy in general.</p><p>The expression as derived is theoretically inapplicable to diffusing sheets for light of normal incidence, but a compensation of errors allows close agreement over the visible range, at 365 millimicrons, and for "white" light, for all except tissue paper and other materials of like transmissivity. For diffuse incidence at 365, and to a certain extent, at 405 millimicrons, some papers show deviations from the simple theory because of fluorescence effects. This and other effects are discussed.</p><p>Reflectances in the infra-red region near 850 millimicrons are also calculated but no standard for comparison is available for these values. The sources of errors at the shorter wave-lengths, however, do not interfere in the infra-red region.</p><p>Transmissions of papers were found to be dependent upon the angle of incidence.</p><p>Reflectances throughout the visible region, measured at 45° from normal incidence were found to agree closely, for the type of papers studied, with those obtained using the General Electric recording spectrophotometer, which corresponds to the conditions of normal incidence and diffuse viewing.</p>

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  1. Kasson S. Gibson, "Survey of spectrophotometers," Paper Trade J. 111 (Sept. 5, 1940)
  2. J. A. Van den Akker, "Survey of abridged spectrophotometers," Paper Trade J. 111 (Sept. 12, 1940).
  3. A. H. Taylor, "Measurement of reflection factors in the ultraviolet," J. Opt. Soc. Am. 21, 776 (1931).
  4. M. Gurevich, "Ueber eine Rationelle Klassification der Lichtstreuenden Medien," Physik. Zeits. 31, 753 (1930).
  5. T. Smith, "The hiding power of diffusing media," Trans. Opt. Soc. 33, 150 (1931–1932).
  6. G. G. Stokes, "On the intensity of light reflected from or transmitted through a pile of plates," Proc. Roy. Soc. (London) 11, 545 (1860–62).
  7. H. J. Channon, F. F. Renwick, and B. V. Storr, "The behavior of scattering media in fully diffused light," Proc. Roy. Soc. (London) A94, 222 (1918).
  8. J. W. Ryde and B. S. Cooper, "Scattering of light by turbid media," Proc. Roy. Soc. (London) A131, 451 (1931).
  9. Frank Benford, "Reflection and transmission by parallel plates," J. Opt. Soc. Am. 7, 1017 (1923).
  10. P. Kubelka and F. Munk, "Ein Beitrag zur Optik der Farbanstriche," Zeits. f. tech. Physik 12, 593 (1931).
  11. F. A. Steele, "Optical characteristics of paper," Paper Trade J. 100 (March 21, 1935).
  12. Deane B. Judd, "Optical specification of light scattering materials," J. Research Nat. Bur. Stand. 19, 287 (1937), RP 1026.
  13. Merle B. Shaw and Martin J. O'Leary, "Effect of filling and sizing materials on stability of book papers," J. Research Nat. Bur. Stand. 21, 671 (1938), RP 1149.
  14. B. A. Brice, "Potentiometer circuit for two barrier layer cells," Rev. Sci. Inst. 8, 279 (1937).
  15. J. S. Preston, "The reflection of magnesium oxide," Trans. Opt. Soc. 31, 15 (1929–30).
  16. Kasson S. Gibson and Harry J. Keegan, "Calibration and operation of the General Electric recording spectrophotometer of the National Bureau of Standards," J. Opt. Soc. Am. 28, 372 (1938).
  17. H. J. McNicholas, "Absolute methods in reflectometry," Bur. Stand. J. Research 1, 50 (1928), RP 3.
  18. Deane B. Judd and Kasson S. Gibson, "Note on the effect of a cover glass in reflectance measurements," J. Research Nat. Bur. Stand. 16, 261 (1936), RP 872.
  19. Institute of Paper Chemistry, Report No. 8, "Adaptability of the G. E. reflection meter as color analyzer." Also in Paper Trade J. 104 (May 6, 1937); (May 13, 1937); (May 20, 1937).

1938 (2)

Merle B. Shaw and Martin J. O'Leary, "Effect of filling and sizing materials on stability of book papers," J. Research Nat. Bur. Stand. 21, 671 (1938), RP 1149.

Kasson S. Gibson and Harry J. Keegan, "Calibration and operation of the General Electric recording spectrophotometer of the National Bureau of Standards," J. Opt. Soc. Am. 28, 372 (1938).

1937 (2)

Deane B. Judd, "Optical specification of light scattering materials," J. Research Nat. Bur. Stand. 19, 287 (1937), RP 1026.

B. A. Brice, "Potentiometer circuit for two barrier layer cells," Rev. Sci. Inst. 8, 279 (1937).

1936 (1)

Deane B. Judd and Kasson S. Gibson, "Note on the effect of a cover glass in reflectance measurements," J. Research Nat. Bur. Stand. 16, 261 (1936), RP 872.

1931 (3)

J. W. Ryde and B. S. Cooper, "Scattering of light by turbid media," Proc. Roy. Soc. (London) A131, 451 (1931).

P. Kubelka and F. Munk, "Ein Beitrag zur Optik der Farbanstriche," Zeits. f. tech. Physik 12, 593 (1931).

A. H. Taylor, "Measurement of reflection factors in the ultraviolet," J. Opt. Soc. Am. 21, 776 (1931).

1930 (1)

M. Gurevich, "Ueber eine Rationelle Klassification der Lichtstreuenden Medien," Physik. Zeits. 31, 753 (1930).

1928 (1)

H. J. McNicholas, "Absolute methods in reflectometry," Bur. Stand. J. Research 1, 50 (1928), RP 3.

1923 (1)

1918 (1)

H. J. Channon, F. F. Renwick, and B. V. Storr, "The behavior of scattering media in fully diffused light," Proc. Roy. Soc. (London) A94, 222 (1918).

Benford, Frank

Brice, B. A.

B. A. Brice, "Potentiometer circuit for two barrier layer cells," Rev. Sci. Inst. 8, 279 (1937).

Channon, H. J.

H. J. Channon, F. F. Renwick, and B. V. Storr, "The behavior of scattering media in fully diffused light," Proc. Roy. Soc. (London) A94, 222 (1918).

Cooper, B. S.

J. W. Ryde and B. S. Cooper, "Scattering of light by turbid media," Proc. Roy. Soc. (London) A131, 451 (1931).

Gibson, Kasson S.

Kasson S. Gibson, "Survey of spectrophotometers," Paper Trade J. 111 (Sept. 5, 1940)

Kasson S. Gibson and Harry J. Keegan, "Calibration and operation of the General Electric recording spectrophotometer of the National Bureau of Standards," J. Opt. Soc. Am. 28, 372 (1938).

Deane B. Judd and Kasson S. Gibson, "Note on the effect of a cover glass in reflectance measurements," J. Research Nat. Bur. Stand. 16, 261 (1936), RP 872.

Gurevich, M.

M. Gurevich, "Ueber eine Rationelle Klassification der Lichtstreuenden Medien," Physik. Zeits. 31, 753 (1930).

Judd, Deane B.

Deane B. Judd, "Optical specification of light scattering materials," J. Research Nat. Bur. Stand. 19, 287 (1937), RP 1026.

Deane B. Judd and Kasson S. Gibson, "Note on the effect of a cover glass in reflectance measurements," J. Research Nat. Bur. Stand. 16, 261 (1936), RP 872.

Keegan, Harry J.

Kubelka, P.

P. Kubelka and F. Munk, "Ein Beitrag zur Optik der Farbanstriche," Zeits. f. tech. Physik 12, 593 (1931).

McNicholas, H. J.

H. J. McNicholas, "Absolute methods in reflectometry," Bur. Stand. J. Research 1, 50 (1928), RP 3.

Munk, F.

P. Kubelka and F. Munk, "Ein Beitrag zur Optik der Farbanstriche," Zeits. f. tech. Physik 12, 593 (1931).

O’Leary, Martin J.

Merle B. Shaw and Martin J. O'Leary, "Effect of filling and sizing materials on stability of book papers," J. Research Nat. Bur. Stand. 21, 671 (1938), RP 1149.

Preston, J. S.

J. S. Preston, "The reflection of magnesium oxide," Trans. Opt. Soc. 31, 15 (1929–30).

Renwick, F. F.

H. J. Channon, F. F. Renwick, and B. V. Storr, "The behavior of scattering media in fully diffused light," Proc. Roy. Soc. (London) A94, 222 (1918).

Ryde, J. W.

J. W. Ryde and B. S. Cooper, "Scattering of light by turbid media," Proc. Roy. Soc. (London) A131, 451 (1931).

Shaw, Merle B.

Merle B. Shaw and Martin J. O'Leary, "Effect of filling and sizing materials on stability of book papers," J. Research Nat. Bur. Stand. 21, 671 (1938), RP 1149.

Smith, T.

T. Smith, "The hiding power of diffusing media," Trans. Opt. Soc. 33, 150 (1931–1932).

Steele, F. A.

F. A. Steele, "Optical characteristics of paper," Paper Trade J. 100 (March 21, 1935).

Stokes, G. G.

G. G. Stokes, "On the intensity of light reflected from or transmitted through a pile of plates," Proc. Roy. Soc. (London) 11, 545 (1860–62).

Storr, B. V.

H. J. Channon, F. F. Renwick, and B. V. Storr, "The behavior of scattering media in fully diffused light," Proc. Roy. Soc. (London) A94, 222 (1918).

Taylor, A. H.

Van den Akker, J. A.

J. A. Van den Akker, "Survey of abridged spectrophotometers," Paper Trade J. 111 (Sept. 12, 1940).

Bur. Stand. J. Research (1)

H. J. McNicholas, "Absolute methods in reflectometry," Bur. Stand. J. Research 1, 50 (1928), RP 3.

J. Opt. Soc. Am. (3)

J. Research Nat. Bur. Stand. (3)

Deane B. Judd and Kasson S. Gibson, "Note on the effect of a cover glass in reflectance measurements," J. Research Nat. Bur. Stand. 16, 261 (1936), RP 872.

Deane B. Judd, "Optical specification of light scattering materials," J. Research Nat. Bur. Stand. 19, 287 (1937), RP 1026.

Merle B. Shaw and Martin J. O'Leary, "Effect of filling and sizing materials on stability of book papers," J. Research Nat. Bur. Stand. 21, 671 (1938), RP 1149.

Paper Trade J. (3)

F. A. Steele, "Optical characteristics of paper," Paper Trade J. 100 (March 21, 1935).

Kasson S. Gibson, "Survey of spectrophotometers," Paper Trade J. 111 (Sept. 5, 1940)

J. A. Van den Akker, "Survey of abridged spectrophotometers," Paper Trade J. 111 (Sept. 12, 1940).

Physik. Zeits. (1)

M. Gurevich, "Ueber eine Rationelle Klassification der Lichtstreuenden Medien," Physik. Zeits. 31, 753 (1930).

Proc. Roy. Soc (1)

H. J. Channon, F. F. Renwick, and B. V. Storr, "The behavior of scattering media in fully diffused light," Proc. Roy. Soc. (London) A94, 222 (1918).

Proc. Roy. Soc. (2)

J. W. Ryde and B. S. Cooper, "Scattering of light by turbid media," Proc. Roy. Soc. (London) A131, 451 (1931).

G. G. Stokes, "On the intensity of light reflected from or transmitted through a pile of plates," Proc. Roy. Soc. (London) 11, 545 (1860–62).

Rev. Sci. Inst. (1)

B. A. Brice, "Potentiometer circuit for two barrier layer cells," Rev. Sci. Inst. 8, 279 (1937).

Trans. Opt. Soc. (2)

J. S. Preston, "The reflection of magnesium oxide," Trans. Opt. Soc. 31, 15 (1929–30).

T. Smith, "The hiding power of diffusing media," Trans. Opt. Soc. 33, 150 (1931–1932).

Zeits. f. tech. Physik (1)

P. Kubelka and F. Munk, "Ein Beitrag zur Optik der Farbanstriche," Zeits. f. tech. Physik 12, 593 (1931).

Other (1)

Institute of Paper Chemistry, Report No. 8, "Adaptability of the G. E. reflection meter as color analyzer." Also in Paper Trade J. 104 (May 6, 1937); (May 13, 1937); (May 20, 1937).

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